Call into the Boar Meeting

I don't think you want a physical device to bridge everyone together as it would require a dedicated telephone line for each person calling in.

Do a Google Search on teleconferencing equipment, conference bridges, or teleconferencing services. In short, the participants can call a local number (or toll-free if you wish) and be connected to a conference bridge (call). You will need to purchase a speakerphone and have access to a telephone line in the library so those attending in person can hear the callers and vice versa. You can use a cell phone in lieu of a dedicated line and connect it to a speakerphone but the sound quality can be variable. Using an external microphone and speaker with the cell phone improves the sound quality.

The service we use for our clients does not have a monthly charge, the calls are charged per minute of use, the number of participants, and how many participants called the toll-free number and not the local number. We believe the rates are quite reasonable.

You should draft ground rules the participants should follow regarding language, etiquette, not speaking when the Board is discussing an agenda item unless invited to provide input, etc.

The only problem that I see with this is if you record your meetings, and people call in on a telephone or Voip service; recording the conversations could be considered wiretapping.
I would consult your HOA attorney and get a SOLID decision from them before conducting call-in meetings.